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Rotations In 3-D
When we performed rotations in two
dimensions we only had the choice of
rotating about the z axis
In the case of three dimensions we have
more options
– Rotate about x – pitch
– Rotate about y – yaw
– Rotate about z - roll

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What Are Projections?
Our 3-D scenes are all specified in 3-D
world coordinates
To display these we need to generate a 2-D
image - project objects onto a picture plane
So how do we figure out these projections?
Picture Plane
Objects in
World Space

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Converting From 3-D To 2-D
Projection is just one part of the process of
converting from 3-D world coordinates to a
2-D image
Clip against
view volume
Project onto
projection
plane
Transform to
2-D device
coordinates
3-D world
coordinate
output
primitives
2-D device
coordinates

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Types Of Projections
There are two broad classes of projection:
– Parallel: Typically used for architectural and
engineering drawings
– Perspective: Realistic looking and used in
computer graphics
Perspective ProjectionParallel Projection

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Types Of Projections (cont…)
For anyone who did engineering or technical
drawing

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Isometric Projections
Isometric projections have been used in
computer games from the very early days of
the industry up to today
Q*Bert Sim City Virtual Magic Kingdom

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Perspective Projections
Perspective projections are much more
realistic than parallel projections

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Perspective Projections
There are a number of different kinds of
perspective views
The most common are one-point and two
point perspectives
ImagestakenfromHearn&Baker,“ComputerGraphicswithOpenGL”(2004)
One Point Perspective
Projection
Two-Point
Perspective
Projection

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The Up And Look Vectors
The look vector
indicates the direction in
which the camera is
pointing
The up vector
determines how the
camera is rotated
For example, is the camera held vertically or
horizontally
Up vector
Look vector
Position
Projection of
up vector